In: Statistics and Probability
1. Out of a sample of 100 purchase orders, 10 contain errors. What is the confidence interval for 95% confidence?
2. For a 95% confidence level, what is the value n (sample size) when π = .15 and the sampling error is .07?
a.99.96
b.61.47
c. 96.04
d.51.00
Explanation:
CONFIDENCE INTERVAL FOR A POPULATION PROPORTION.
n=100
x=10(Sample size, Number of trials).(Number of success).
1−α=0.95(Confidence level).
Choice of statistic
Confidence interval for a population proportion.
If p^ is the proportion of observations in a random sample of size n that belongs to a class of interest, a 100 (1−α)%confidence interval on the proportion p of the population that belongs to this class is:
Sample proportion.
Calculus of zα/2− value.
1−α=0.95
α=1−0.95
α=0.05
α/2=0.05/2
α/2=0.0250
Calculus of zα/2 using the cumulative standard normal distribution
table.
We search through the probabilities to find the value that corresponds to 0.9750.
we find 0.9750 exactly, therefore
zα/2 =1.9+0.06=1.96
Calculus of the confidence interval using the direct method.
(2)
1−α=0.95 (Confidence level)
E=0.07 (Error)
p^=0.15..(Initial estimate of p)
Sample size.
Calculus of zα/2− value.
1−α=0.95
α=1−0.95
α=0.05
α/2=0.05/2
α/2=0.0250
Calculus of zα/2 using the cumulative standard normal distribution table.
We search through the probabilities to find the value that corresponds to 0.9750.